There are many kinds of prior art folding umbrellas which include central shafts and sets of frame linkages. Known folding umbrellas should be used with ease and have a small volume when closed. Prior art systems are exemplified for example in U.S. Pat. Nos. 4,739,783 and 4,676,262. In such systems the frame linkages consist of several straight ribs and sticks. When the frame linkage is folded, the end of the first rib will be convexly deformed and resists the movement of the second stick. Thus, the outer ribs and sticks cannot be effectively and easily moved inwardly while the whole umbrella occupies a larger volume than necessary.